Method and device for beam analysis

ABSTRACT

A method and an apparatus for beam analysis in an optical system are disclosed, wherein a plurality of beam parameters of a beam propagating along an optical axis are ascertained. The method includes: splitting the beam into a plurality of partial beams which have a focus offset in the longitudinal direction in relation to the optical axis; recording a measurement image produced by these partial beams; carrying out a forward simulation of the beam in the optical system on the basis of estimated initial values for the beam parameters in order to obtain a simulated image; and calculating a set of values for the beam parameters on the basis of the comparison between the simulated image and the measurement image.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of, and claims benefit under35 USC 120 to, international application PCT/EP2016/073785, filed Oct.5, 2016, which claims benefit under 35 USC 119 of German Application No.10 2015 219 330.6, filed on Oct. 7, 2015. The entire disclosure of theseapplications are incorporated by reference herein.

FIELD

The disclosure relates to a method and an apparatus for beam analysis inan optical system. In particular, the disclosure can be used to alsoobtain information about possible wavefront deviations in the case of alaser beam by way of an analysis of the geometric beam parameters (suchas spatial orientation and tilt) and to correct these, optionally inreal time, during the operation of the respective optical system.

The disclosure is suitable for analyzing electromagnetic radiation, asis used in e.g. laser plasma sources (for example, in the case of an EUVsource of a microlithographic projection exposure apparatus), but it isnot restricted thereto. In further applications, the disclosure is alsogenerally suitable for analyzing electromagnetic radiation which is usedfor any desired purposes (in particular measurement purposes ordiagnostic purposes).

BACKGROUND

Many laser applications involve knowledge that is as accurate aspossible with respect to beam parameters such as e.g. the beam size,beam decentration, beam inclination or beam divergence, and also involvethe correction of aberrations (such as e.g. astigmatism, coma andspherical aberration).

An issue occurring here in practice is that, e.g., thermally inducedwavefront changes or aberrations of the laser beams may occur, knowledgeabout which that is as exact as possible being involved for a correctionthat takes place during the operation (in real time).

However, in this case, the use of sensors that are conventionally usedfor wavefront measurement (such as, e.g., so-called Shack-Hartmannsensors with a CCD camera situated in the focal plane of the microlensarrangement) only has restricted suitability to the extent that, onaccount of the geometric reference centers (e.g., vertices or aperturesof the lenses in the microlens arrangement in the case of aShack-Hartmann sensor) that have been introduced, as a matter ofprinciple, by the measurement arrangement, the respective measurementresult is also influenced by effects which are based on the interactionor shearing of the coordinate system of the laser radiation on the onehand with the coordinate system of the measurement arrangement on theother (such that the intrinsic coordinate system inherent to themeasurement arrangement is virtually “impressed” onto the measurementresult). This has as a consequence, in particular, that beamdisturbances occurring during the measurement, for instance as aconsequence of a positional change of the measurement arrangementrelative to the laser beam, are immediately noticeable in themeasurement result and, in this respect, make a reliable wavefrontanalysis more difficult, or prevent the latter, since it is notdeterminable whether a measured wavefront effect is based on an actuallyoccurred (e.g. thermally induced) wavefront modification or only basedon a positional change (e.g. “wobbling”) of the measurement arrangementrelative to the laser beam.

Expressed differently, there is a need during the analysis of wavefrontaberrations of a laser beam to ascertain the wavefront aberrations inthe coordinate system of the laser beam itself (and not in that of themeasurement arrangement).

Moreover, there is also a need to obtain the corresponding resultssufficiently quickly during the operation of the respective system inorder to be able to promptly correct possible wavefront aberrations, forinstance using an adaptive mirror or the like.

A purely exemplary laser application is the laser plasma source which isused in e.g. lithography for producing EUV light (e.g. at wavelengths ofe.g. approximately 13 nm or approximately 7 nm) and with respect towhich FIG. 12 shows a schematic illustration of the possibleconstruction. The EUV laser plasma source according to FIG. 12 has ahigh-energy laser (not shown here) e.g. for generating infraredradiation 6 (e.g. a CO₂ laser with a wavelength of λ≤10.6 μm), theinfrared radiation being focused by way of a focusing optical unit,passing through an opening 11 present in a collector mirror 10 embodiedas an ellipsoid and being guided onto a target material 32 (e.g. tindroplets) which is generated via a target source 35 and supplied to aplasma ignition position 30. The infrared radiation 6 heats the targetmaterial 32 situated in the plasma ignition position 30 in such a waythat the target material transitions into a plasma state and emits EUVradiation. This EUV radiation is focused by way of the collector mirror10 onto an intermediate focus IF and enters through the latter into adownstream illumination device, the edge 40 of which is merely indicatedand which has a free opening 41 for the light entrance.

Both the droplet position of the (e.g., tin) droplets forming the targetmaterial and the focus position of the laser beams to be trackedaccordingly can be determined using a so-called beam propagation camera,wherein both the laser beams in the “forward direction” (the infraredradiation 6 prior to incidence on the respective target droplets) andthe laser beams in the “backward direction” (the infrared radiation 6reflected back from the respective target droplet) are detected and themeasurement data involved for the laser beam guidance and dropletguidance are obtained. Here, there is a need to be able to promptlycorrect thermally induced aberrations, involving an accurate and fastanalysis of the laser beams.

With regard to the prior art, reference is made by way of example to WO2015/113713 A1.

SUMMARY

The disclosure seeks to provide a method and an apparatus for beamanalysis, which facilitate a reliable analysis that is effectuatedsufficiently quickly and as free from disturbances as possible.

In an aspect, the disclosure provides a method for beam analysis in anoptical system, wherein a plurality of beam parameters of a beampropagating along an optical axis are ascertained. The method includesthe following steps: a) splitting the beam into a plurality of partialbeams which have a focus offset in the longitudinal direction inrelation to the optical axis; b) recording a measurement image producedby these partial beams; c) carrying out a forward simulation of the beamin the optical system on the basis of estimated initial values for thebeam parameters in order to obtain a simulated image; and d) calculatinga set of values for the beam parameters on the basis of a comparisonbetween the simulated image and the measurement image.

In an aspect, the disclosure provides an apparatus beam analysis in anoptical system, having at least one beam-splitting optical arrangement,which brings about beam splitting of a beam, incident on thebeam-splitting optical arrangement along an optical axis duringoperation, into a plurality of partial beams which have a focus offsetin a longitudinal direction in relation to the optical axis, and atleast one sensor arrangement for capturing these partial beams.

A method according to the disclosure for beam analysis in an opticalsystem, wherein a plurality of beam parameters of a beam propagatingalong an optical axis are ascertained, includes the following steps:

-   -   splitting the beam into a plurality of partial beams which have        a focus offset in the longitudinal direction in relation to the        optical axis,    -   recording a measurement image produced by these partial beams,    -   carrying out a forward simulation of the beam in the optical        system on the basis of estimated initial values for the beam        parameters in order to obtain a simulated image, and    -   calculating a set of values for the beam parameters on the basis        of the comparison between the simulated image and the        measurement image.

Within the scope of the present application, “splitting a beam into aplurality of partial beams” should be understood to mean that thesepartial beams each constitute a copy of the original split beam to theextent that the partial beams in each case have the same geometricparameters as the original beam, with only the intensity of the partialbeams being correspondingly reduced in relation to the intensity of theoriginal beam as a result of the split into a plurality of partialbeams. As a result, the beam-splitting optical arrangement is used toreplicate the beam to be analyzed into a plurality of partial beams in asuitable manner, wherein a sensor arrangement with a suitable extent canbe used to simultaneously record a plurality of beam sections ormeasurement spots.

According to an embodiment, the method further includes the steps of:

-   -   iteratively performing the steps of the forward simulation and        of calculating a set of values for the beam parameters, wherein        the respectively calculated values for the beam parameters form        the basis of a forward simulation that follows in each case, and    -   outputting output values for the beam parameters, ascertained by        this iteration.

Consequently, according to an embodiment of the disclosure, thecalculation of a set of values for the beam parameters is effectuated,in particular iteratively, on the basis of the plurality of comparisonsbetween recorded measurement images and calculated or simulated images.This takes account of the fact that unavoidable interferences occurbetween the measurement images (“spot images”) assigned to theindividual, different focus positions, wherein the interferences may, inparticular, lead to comparatively large mutual disturbances of thespots. The individual measurement images assigned to different focuspositions cannot simply be considered to be independent of one anotheron account of the mutual disturbances, which in turn is an obstacle to a“separate” forward and backward propagation—in which, for example, thecomponents of the beam-splitting optical arrangement assigned to theindividual focus positions are considered to be decoupled or areconsidered independently—through the optical system or which prevents acorrect back calculation to the beam parameters.

According to an embodiment, the method further includes the step ofrecording a near-field image produced by the beam.

Recording the near-field image and recording a far-field image thatcorresponds to the measurement image produced by the partial beams maybe effectuated at the same time. Further, use can also be made of morethan one sensor arrangement for recording the measurement images (e.g. asensor arrangement for recording the near-field image and a furthersensor arrangement for recording the far-field image).

Here, “near field” denotes the amplitude or intensity distribution in asectional plane perpendicular to the direction of propagation in theregion of the collimated beam (i.e. expanded or virtuallydivergence-free beam). The “far field”, by contrast, corresponds to theamplitude or intensity distribution in a plane near the waist, or nearthe focus, perpendicular to the beam propagation in the region of thefocused or convergent beam.

Recording the near-field image renders it possible to directly determinethe absolute value component of the complex amplitude function (assquare root of the intensity) for the beam to be analyzed, immediatelyin the near field. This is particularly advantageous to the extent thatthe absolute value of the amplitude can only be determined withdifficulties from the far-field image (i.e. the image close to the focusafter passing through the beam-forming and beam-splitting optics) sincethe focusing properties or far-field images are substantially dominatedby the phase of the electromagnetic radiation and the absolute value ofthe amplitude in the far field is only poorly accessible. Consequently,the disclosure explicitly takes account of the fact that near field andfar field, in a sense, carry complementary information to the extentthat they image different aspects of the complex amplitude function. Aconsequence of the concept according to the disclosure is thatsubstantially only the wavefront or the phase of the complex amplitudestill needs to be determined from the far-field image. Therefore, as aresult, the reconstruction result in the case of the additionalconsideration of the near-field information according to the disclosureis improved significantly when compared to only taking account of thefar-field information.

The circumstance that, according to the disclosure, the completeinformation for the beam evaluation is already supplied by a singlerecording effectuated by a sensor arrangement (i.e. the simultaneousrecording of a near-field image and a far-field image) has the furtheradvantage that, in the case of e.g. a pulsed laser or else in the caseof other laser types (such as e.g. CW-lasers) with pronouncedfluctuations in the beam properties, it is possible to carry outindividual (e.g. pulse-resolved) wavefront analyses (in a sense as“single shot” measurements).

According to an embodiment, the plurality of beam parameters includes atleast one of the following parameters: beam size, beam decentration,beam inclination, beam divergence, astigmatism, coma, sphericalaberration, and possibly further parameters as well.

The aberrations may be of any order and, for example, may be describedin a hierarchic function system that is ideally adapted to the symmetry(e.g. Zernike polynomials).

According to an embodiment there is, on the basis of the output valuesfor the beam parameters, a manipulation of the beam while adapting atleast one of the beam parameters.

According to an embodiment, outputting the output values and adapting atleast one of the beam parameters are effectuated in real time during theoperation of the optical system.

Within the scope of the iterative performance of the steps of theforward simulation and of calculating a set of values for the beamparameters, the number of varied beam parameters is varied, inparticular reduced, according to an embodiment.

Here, the disclosure contains the further concept of adapting the scopeof the model by using the respectively previously ascertained imagewithin the meaning of an adaptive procedure.

On account of this, it is possible to take account of the fact thatenabling a large number of parameters when iteratively performing thesteps of the forward simulation and of calculating a set of values forthe beam parameters leads to a high numerical complexity, which may,under certain circumstances, be opposed to determining and adapting thebeam parameters in real time (e.g. the beam adaptation in a laser plasmasource). Preferably, there may initially be, for example, a start with acomparatively small scope of the parameters set, which is thensuccessively expanded with respect to the simultaneously variedparameters within the further course of the iteration of the parametersset (i.e. adaptive fitting of the model is undertaken).

Within the scope of the iterative performance of the steps of theforward simulation and of calculating a set of values for the beamparameters, an algorithm used in this iteration is varied according toan embodiment.

By way of example, a faster evaluation method for obtaining the highestpossible speed in the beam analysis may be selected after reaching aquasi-stationary operation of the respective system (e.g. the plasmalight source), during which there only still are small changes in thebeam parameters. Here, in particular, use can be made of the informationalready collected previously in order then to be able to determine andcorrect, in real time, the small changes in the beam parameters thatstill occur.

As a result, what may be achieved thus is that, for instance in a plasmalight source, the laser beam can be guided, accurately and quickly atthe same time, with respect to the beam parameters since, for example,thermally induced aberrations can be corrected promptly.

According to an embodiment, the beam is split using a beam-splittingoptical arrangement, which brings about spherical wavefront deformationsof the beam. Here, the disclosure is based on the further concept ofrealizing a wavefront determination on the basis of a split, obtained byspherical wavefront deformations of the beam, into a plurality ofpartial beams, which are assigned to different focus positions.

As a result of only spherical wavefront deformations of the beam beingperformed for splitting the beam, the impression of an additionalcoordinate system on account of the measurement arrangement and, hence,an unwanted interaction or shearing of such a coordinate system with thecoordinate system of the laser radiation are avoided. Here, thedisclosure proceeds from the idea that a spherical wavefront does nothave a center or a point that is marked out in any way on account of thecurvature that is constant at each point such that no special coordinatesystem, which may be impressed onto the coordinate system of the laserradiation, is produced either by way of a measurement arrangementconstructed in such a way. In principle, an optical system that onlycauses spherical wavefront deformations of the beam may be constructedfrom lens elements, but also, for example, from a diffractive opticalelement.

In accordance with an embodiment, the beam-splitting optical arrangementhas at least one diffractive structure.

Here, the disclosure further contains the concept of, by using adiffractive structure, obtaining the plurality of focus positions whichare generated by such a diffractive structure and which correspond tothe different orders of diffraction of the diffractive structure inorder to realize the longitudinal focus offset. In other words, thedisclosure makes use in a targeted manner of the usually unwantedproperty of a diffractive lens element of generating mutually differentfocus positions in accordance with the different orders of diffractionin order to realize a longitudinal focus offset for beam analysis. Atthe same time, the disclosure makes use of the further circumstance thata lateral offset of the partial beams beyond the aforementionedlongitudinal focus offset for enabling simultaneous recording at thelocation of the sensor arrangement is achievable in a comparativelysimple manner by way of a “break in symmetry” which, for example, can beobtained by a simple decentration of the diffractive structure (eitherby displacement in a plane perpendicular to the optical axis or alreadyby an appropriate design of the diffractive structure).

According to an embodiment, the beam-splitting optical arrangement isdesigned in such a way that it splits a beam incident on the arrangementinto partial beams, wherein the points of incidence of these partialbeams form a two-dimensional, grid-like distribution on a planeextending transversely to the light propagation direction of the beam(wherein this plane may be, in particular, the detector plane in whichthe aerial image is produced). Here, the points of incidence may bedefined as the geometric center of the respective centroid rays or aspoints of the respective partial beams that are distinguished in anothersuitable way. Furthermore, the term “two-dimensional, grid-likedistribution” should also include non-regular or non-periodictwo-dimensional distributions.

According to an embodiment, the beam-splitting optical arrangement hasat least two diffractive structures, which extend in mutually differentdirections, in particular mutually perpendicular directions.

Such a configuration of the beam-splitting optical arrangement accordingto the disclosure was found to be advantageous in multiple respects,wherein reference should be made in this context to, first of all, themore efficient fill of a sensor or detector plane (which typicallyextends in two planes). However, moreover, a significant increase of themeasurement range with an unchanging high resolution may be obtained inthe case of a suitable design of the beam-splitting optical arrangementor of the diffractive structures provided therein—as will still beexplained in more detail below. This measurement range increase may, inturn, serve firstly to increase the “capture region” with respect tocapturable focus values of the beam to be analyzed in the case of anunchanging high resolution (namely under the provision of a sufficientnumber of measurement points in the relevant focus region). In this way,it is possible to take account of the comparatively large focusvariations of the beam to be characterized, as occur as a consequence ofheating and deformation of the individual optical components in, forexample, applications of material processing or else the laser plasmasource, described at the outset, in the case of high laser powers. Here,it may be possible, under certain circumstances, to also realize anISO-compliant beam characterization to the extent that a sufficientnumber of measurement points are respectively obtained both in theimmediate vicinity of the focus of the beam to be analyzed and also at asufficient distance from this focus. Secondly, if desired, a redundancywith respect to the provided measurement points or focus values may beobtained within the respectively covered measurement range—as willlikewise still be explained in more detail below—which, in turn, can beused to calibrate the measurement system.

According to an embodiment, these diffractive structures differ by atleast a factor of 3, in particular by at least a factor of 4, furtherparticularly by at least a factor of 5, in terms of their focal lengthrelated to the first positive order of diffraction in each case.

According to an embodiment, the optical system is a laser plasma source.

However, the disclosure is not restricted thereto but applicable in manyother fields. By way of example, an application may be effectuated inlaser metrology (e.g. wherever Shack-Hartmann sensors are conventionallyused). Further advantageous applications of the disclosure relates tomedical engineering, material processing and communication technology.

Further, the disclosure relates to an apparatus for beam analysis in anoptical system, having at least one beam-splitting optical arrangement,which brings about beam splitting of a beam, incident on thebeam-splitting optical arrangement along the optical axis duringoperation, into a plurality of partial beams which have a focus offsetin a longitudinal direction in relation to the optical axis, and atleast one sensor arrangement for capturing these partial beams.

The disclosure further also relates to a beam-splitting opticalarrangement, wherein the arrangement brings about beam splitting of abeam, incident on the beam-splitting optical arrangement along theoptical axis during operation, into a plurality of partial beams whichhave a focus offset in a longitudinal direction in relation to theoptical axis, wherein the points of incidence of these partial beamsform a two-dimensional, grid-like distribution on a plane extendingtransversely to the light propagation direction of the beam.

The apparatus according to the disclosure for beam analysis or thebeam-splitting optical arrangement may be configured, in particular, forcarrying out a method having the features described above. With regardto advantages and preferred configurations of the apparatus and thearrangement, reference is made to the explanations above in conjunctionwith the method according to the disclosure.

However, the apparatus or arrangement is not restricted to theapplication in the above-described method. The apparatus or arrangementis also usable in applications in which a focus reconstruction (withrespect to focus position and focus size) can be performed withoutreconstructing the phase.

Further configurations of the disclosure can be gathered from thedescription and the dependent claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure is explained in greater detail below on the basis ofexemplary embodiments illustrated in the accompanying figures, in which:

FIG. 1 shows a schematic illustration of a measurement arrangement usedin an exemplary manner in a method according to the disclosure;

FIGS. 2A and 2B show a schematic illustration (FIG. 2A) and a diagram(FIG. 2B) for explaining construction and functionality of an exemplaryembodiment of a beam-splitting optical arrangement;

FIG. 3 shows a schematic illustration of a further embodiment of ameasurement arrangement used in an exemplary manner in a methodaccording to the disclosure;

FIGS. 4 and 5 show schematic illustrations for explaining the possiblesequence of a method according to the disclosure;

FIGS. 6A and 6B show schematic illustrations for explaining a problemunderlying the disclosure.

FIGS. 7, 8A-8E, 9, 10, 11A, 11B and 11C show schematic illustrations forexplaining further embodiments of the disclosure; and

FIG. 12 shows a schematic illustration of the design of an EUV lightsource in accordance with the prior art.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

According to FIG. 1, a beam to be analyzed, which is produced by a laserlight source (not depicted here) and comes from a telescope unit 101(which has, inter alia, an attenuator 102 in FIG. 1), is initiallyincident on an optical beam splitter 103 in an exemplary measurementarrangement, part of the beam being decoupled immediately by the opticalbeam splitter and being steered onto a sensor arrangement 120 (e.g. Inthe form of a CMOS arrangement or a CCD arrangement). The portiontransmitted through the beam splitter 103 reaches a beam-splittingoptical arrangement 110 via deflection mirrors 104, 106 (between which afurther attenuator 105 is arranged) and the sensor arrangement 120 fromthe beam-splitting optical arrangement via a further deflection mirror107. Consequently, according to FIG. 1, a near-field image that isproduced by the immediately decoupled part of the beam is also recordedin addition to the far-field image that is produced by the part of thebeam that is steered via the beam-splitting optical arrangement 110. Asalready explained, this is advantageous in that the absolute value ofthe amplitude is already present in an immediate form and therefore itis only still involved to substantially determine the wavefront or thephase of the complex amplitude by way of a retrieval scheme yet to beexplained below.

In the exemplary embodiment, as indicated in FIG. 2A, the beam-splittingoptical arrangement 110 has a diffractive structure 111 and a refractiveoptical element (refractive lens element) 112, which have a monolithicembodiment here and together form a multi-focal optical element. In aspecific exemplary embodiment, the refractive optical element 112 can bea plano-convex lens element, wherein the diffractive structure 111 canbe formed on the plane surface of this plano-convex lens element. Thediffractive structure and refractive optical element or lens element canalso have a separate configuration and a (preferably small) distancefrom one another in further embodiments. In principle, in accordancewith the occurring orders of diffraction, a diffractive lens element haspositive and negative focal lengths in accordance with

$\begin{matrix}{{f_{diff} = \frac{f_{1}}{k}},{k = 0},{\pm 1},{\pm 2},\ldots} & (1)\end{matrix}$

Here, f₁ denotes the focal length of the first positive order ofdiffraction and k denotes the beam index or the order of diffraction.Here, the intensity of the respective focus depends directly on theembodiment and approximation form of the underlying (approximatelyparabolic) phase profile. In combination with a refractive lens elementwith a focal length of f₀, a multi-focal optical system emerges with aplurality of used focal lengths f_(k), k=0, ±1, . . . , k_(max), whereinthe following applies approximately if the distance between thediffractive structure and the refractive lens element is neglected:

$\begin{matrix}{f_{k} \approx \frac{f_{0}f_{1}}{f_{1} + {kf}_{0}}} & (2)\end{matrix}$

This relation is elucidated in FIG. 2B for f₁>>f₀.

The disclosure is not restricted to the configuration of thebeam-splitting optical arrangement 110 with such a diffractivestructure. Rather, what is important in the configuration of thebeam-splitting optical arrangement is that it causes, where possible,spherical wavefront deformations of the beam that is incident on thebeam-splitting optical arrangement. In further embodiments, use may alsobe made of a different beam-spitting optical arrangement suitable tothis end, for example in the form of an etalon.

The partial beams emanating from the beam splitting optical arrangementare thereupon incident on—reference once again being made to FIG. 1—thesensor arrangement 120, on which different spot images corresponding tothe focus offset are produced, the size of the spot images beingsmallest in the middle or in the perfect focus in the shown example andincreasing toward the edge. The recording produced by the sensorarrangement 120 is denoted “121”.

FIG. 3 shows a further embodiment of a measurement arrangement, whereincomponents analogous or substantially functionally identical to FIG. 1are designated by reference numerals increased by “200”. The embodimentof FIG. 3 differs from that of FIG. 1 in that provision is made here ofa diffractive structure 310 in the form of a reflective element, withprovision further being made of a spherical deflection mirror 307.

In principle, the recording of these individual spot images assigned todifferent focus positions in each case by the application of known,so-called “phase retrieval” methods (e.g. Gerchberg-Saxton algorithm)would allow a back calculation to the phase of the wave-front if theindividual spot images were independent of one another (i.e. if therewere no mutual influencing by way of interference). However, unavoidableinterferences between the individual spot images are present in thiscase, the interferences leading to a pronounced mutual disturbance asindicated in FIG. 6 (with FIG. 6A showing ideal spot images withouttaking account of the interference and FIG. 6B showing real spot imageswith taking account of the interference).

Mathematically, these circumstances mean that no unique backtransformation is possible for directly calculating the beam parameters.In order to take account of this problem, iterative comparisons betweenrespectively calculated or simulated images and the recorded measurementimage are performed according to the disclosure in a model-basedapproach, as described below with reference to FIG. 4 and FIG. 5:

As indicated in the schematic diagram of FIG. 4, this is initially basedon estimated values for the sought-after beam parameters (step S410),with the corresponding parameters set being denoted by a₁, a₂, a₃, . . .in this case.

These parameters for describing the beam may be, for example, the beamsize, beam decentration in the x-direction, beam decentration they-direction, beam inclination in the x-direction, beam inclination inthe y-direction, beam divergence, astigmatism in the x-direction,astigmatism in the y-direction, coma in the x-direction, coma in they-direction and spherical aberration. Here, a Zernike parameterizationmay also be effectuated when desired in order to describe and ascertaincorresponding wavefront aberrations of higher order too.

Thereupon there is a forward simulation (step S420) for ascertaining acalculated image. According to FIG. 5, this forward simulation includes,in particular, a free space propagation P₁ in the form of a Fouriertransform upstream of the beam-splitting optical arrangement 110 or 310(with respect to the light propagation direction) and a free spacepropagation P₂, likewise in the form of a Fourier transform, downstreamof the beam-splitting optical arrangement 110 or 310 (with respect tothe light propagation direction), which each act on the complexamplitude function u=√{square root over (I·e^(iφ))}.

If the assumption of a beam propagation in the positive z-direction ismade, the beam amplitude to be determined z₀ in the range of scalardiffraction) is denoted by u(x,y|z₀) at the location z₀ in the referenceplane (ideally near-field plane). After passing over the free space pathbetween the reference plane and the plane of the effective opticalelement (beam-splitting optical arrangement 110 or diffractive opticalstructure), the amplitude present at the entrance of the optical elementforming the beam-splitting optical arrangement 110 or 310 at theposition z₁ is given by

u(x,y|z ¹⁻)={circumflex over (P)} ₁ u(x,y|z ₀)=IFT _(xy)[Π(z ₁ −z ₀)·FT_(xy) [u(x,y|z ₀)]]  (3).

The optical element forming the beam-splitting optical arrangement 110or 310, in the approximation of the infinitely thin element,multiplicatively impresses the amplitude functionT(x,y)=t(x,y)·exp(iφ(x,y))u(x,y|z¹⁻) according to

u(x,y|z ₁₊)=T(x,y)u(x,y|z ¹⁻)  (4).

By way of a further free space propagation from the optical elementforming the beam-spitting optical arrangement 110 or 310 to the sensorarrangement 120 or 320 (the plane of which lies perpendicular to thez-axis at the position z₂), the amplitude on the plane of the sensorarrangement 120 or 320 is finally arrived at according to

u(x,y|z ₂)={circumflex over (P)} ₂ u(x,y|z ₁₊)=IFT _(xy)[Π(z ₂ −z ₁)·FT_(xy) [u(x,y|z ₁₊)]]  (5)

The intensity profile detected at the spatially-resolving sensorarrangement 120 or 320 is obtained by forming the square of the absolutevalue according to

I _(Sensor)(x,y)=|u(x,y|z ₂)|²  (6)

The propagator of the free space propagation is known from the formalismof Fourier optics. During the propagation from a plane perpendicular tothe z-axis at the position z′ to a parallel plane at the position z, theamplitude is initially transformed into the frequency space according to

ũ(f _(x) ,f _(y) |z′)=FT _(xy) [u(x,y|z′)]=∫∫dxdyu(x,y|z′)exp(−2πi(f_(x) x+f _(y) y))  (7)

by way of the 2D Fourier transform and there it is multiplied by thefree space propagation function

$\begin{matrix}{{\Pi \left( {\left. d \middle| f_{x} \right.,f_{y}} \right)} = {\exp \left( {2\pi \; i\; \frac{d}{\lambda}{\gamma \left( {f_{x},f_{y}} \right)}} \right)}} & (8)\end{matrix}$

over the distance d=z−z′. Here, the phase in the propagation function isgiven by

γ(f _(x) ,f _(y))=√{square root over (1−λ²(f _(x) ² +f _(y) ²))}  (9),

where f_(x),f_(y) denote the spatial frequencies and λ denotes thewavelength of the radiation. The amplitude in the plane at z in thespatial domain is finally obtained by a back transformation by way ofthe inverse Fourier transform according to

$\begin{matrix}{{u\left( {x,\left. y \middle| z \right.} \right)} = {\underset{A}{\int\int}{dxdy}\; {\Pi \left( {\left. {z - z^{\prime}} \middle| f_{x} \right.,f_{y}} \right)}{u\left( {f_{x},\left. f_{y} \middle| z^{\prime} \right.} \right)}{\exp \left( {{+ 2}\pi \; {i\left( {{f_{x}x} + {f_{y}y}} \right)}} \right)}}} & (10)\end{matrix}$

The correspondingly calculated image (containing the calculatedintensity values I_(calc)) is subtracted from the recorded measurementimage (containing the measured intensity values I_(meas)), whereuponappropriately modified model parameters for describing the beam areascertained and these form the basis of a new forward simulation (stepS460 in FIG. 4). Here, an optimization is performed, for example byapplying a Levenberg-Marquardt algorithm. Thereupon, according to FIG.5, the calculated intensity values I_(calc) are ascertained anew by aforward simulation, with a new calculated image being obtained thereby,wherein the difference between the calculated image and the recordedmeasurement image is ascertained again. This is carried out iterativelyuntil the difference between the calculated image and the recordedmeasurement image is sufficiently small (or falls below a predeterminedthreshold), whereupon the appropriate parameters for describing the beamare output.

As already explained above, it is particularly advantageous if theabsolute value of the amplitude is available from the near-fieldmeasurement and if it need not be described and fitted by a model. As aresult, firstly, the number of parameters to be described is reduced,possibly significantly reduced, and, secondly, the quality of theinformation obtained about the beam to be measured is improved.

According to the disclosure, the fact that enabling a large number ofparameters leads to high numerical complexity is preferably furthertaken into account. Consequently, there preferably is initially a startwith a comparatively small scope of the parameters set, which is thensuccessively expanded with respect to the simultaneously variedparameters of the parameters set, i.e. adaptive fitting of the model isundertaken. Thus, for instance, if twenty parameters are sought after inprinciple, only ten dominating parameters may initially be enabled.

Furthermore, it is also possible to adapt the respective evaluationmethod or the algorithm in order to obtain the fastest possible speedfor the beam analysis, for example after reaching a quasi-stationaryoperation of the respective system (e.g. a largely stably operatedplasma light source), in which, typically, only small changes in thebeam parameters still occur. Here, in particular, use can be made of thealready collected information in order then to be able to determine andcorrect, in real time, the small changes in the beam parameters thatstill occur. In this phase, the originally nonlinear optimizationproblem may also be approximable in linear form. As a result, what maybe achieved thus is that, for instance in a plasma light source, thelaser beam can be guided, accurately and quickly at the same time, withrespect to the beam parameters.

FIGS. 7-11 show schematic illustrations for explaining furtherembodiments of the disclosure. What is common to these embodiments isthat, in this case, the beam-splitting optical arrangement according tothe disclosure is configured in such a way that the beam splitting iseffectuated in a “two-dimensional” manner to the extent that the beamswith a longitudinal focus offset relative to one another that wereproduced during this split form, with respect to the points of incidenceon the plane, a two-dimensional grid-like arrangement in, in each case,a plane transverse to the light propagation direction andhence—according to an aspect of this configuration—they are suitable, inparticular, for effectively filling a two-dimensional sensor or detectorarea. According to a further aspect of this configuration, a significantmeasurement range increase can also be obtained hereby, as will bedescribed in more detail below.

In order to obtain this two-dimensional beam split, it ispossible—without the disclosure being restricted hereto—to provide, forexample in the embodiment schematically illustrated in FIG. 7, twodiffractive optical elements 711, 712, of which, in turn, the onediffractive element 711 is arranged in an exemplary manner upstream of arefractive optical element (refractive lens element) 713, which ispresent in a manner analogous to the embodiment of FIG. 2A, in relationto the light propagation direction (extending in the z-direction in theplotted coordinate system) and the other diffractive optical element 712is arranged downstream of this refractive optical element 713. Infurther embodiments (some of which are schematically illustrated inFIGS. 8A-8E), the diffractive structure involved for the two-dimensionalbeam split may also be realized in any other suitable manner.

The mode of operation of the beam-splitting optical arrangementaccording to FIG. 7 formed by the diffractive optical elements 711, 712and the refractive optical element 913 is elucidated in FIG. 9 (whereanalogous or functionally equivalent components are denoted by referencesigns that have been increased by “200”). Accordingly, according to FIG.9, the first diffractive optical element 911 produces a split of theincident beam with fanning into partial beams which diverge in thexz-plane and the second diffractive optical element 911 produces a splitwith fanning into partial beams which diverge in the yz-plane. Theresultant two-dimensional beam distribution obtained in the sensor ordetector plane is denoted by “950”.

Proceeding from the basic construction of the beam-splitting opticalarrangement according to FIG. 7 or FIG. 9, FIG. 10 shows a schematicillustration for explaining an exemplary geometric design. The twoaforementioned diffractive optical elements are only indicated here bythe respective planes 1011 and 1012, wherein, at the same time, adecentration by offsetting the respective diffractive structure in aplane perpendicular to the optical axis, respectively by distance“d_(x)” or “d_(y)” is indicated for the purposes of obtaining a lateraloffset of the partial beams (“break of symmetry”). In FIG. 10, “1001”denotes the entrance plane of the beam and “1015” denotes the sensor ordetector plane.

Analogous to the embodiment of FIG. 2A, the multifocal optical systemformed by the beam-splitting optical arrangement according to FIG. 7 or9 has a plurality of used focal lengths, wherein the followingapproximately applies if the distance between the diffractive opticalelements and the refractive lens element is neglected here:

$\begin{matrix}{f_{m,n} \approx \frac{f_{0}f_{1}^{*}f_{2}^{*}}{{f_{1}^{*}n} + {f_{2}^{*}m} + {f_{0}{mn}}}} & (11)\end{matrix}$

Here, f₁* and f₂* denote (in relation to the respective first positiveorder of diffraction) the respective focal lengths of the firstdiffractive optical element 911 and the second diffractive opticalelement 912, respectively, and f₀ denotes the focal length of therefractive optical element 913, while “m” and “n” denote the orders ofdiffraction of the respective diffraction at the first optical element911 and second diffractive optical element 912, respectively.

The focal lengths of the first diffractive optical element 911 and thesecond diffractive optical element 912 are selected to be different fromone another, with the consequence that the element with the relativelyshorter focal length produces the relatively greater longitudinal focusoffset, and vice versa. In a specific exemplary embodiment, it ispossible, for instance, for the focal length of the first diffractiveoptical element 911 to be greater by a factor of five than the focallength of the second diffractive optical element 912.

In the case of a suitable selection of the aforementioned parameters(i.e. the focal lengths f₁*, f₂* and f₀) and of the used value ranges ofthe orders of diffraction (n, m), it is now possible to obtain and use ameasurement range increase in different ways, as will be explained belowwith reference to FIGS. 11A-11C.

FIG. 11A initially shows a possible distribution of focal lengthsobtained over the individual fanned beams using a beam-splitting opticalarrangement according to the disclosure in accordance with FIG. 7 or 9.Here, a value group “A”, “B”, “C”, . . . of in each case seven values orpoints in the diagram (corresponding to the number of orders ofdiffraction in the value range of −3 to +3 selected in an exemplarymanner) in each case corresponds to a line in the two-dimensional beamdistribution obtained in the sensor or detector plane. Firstly, it isclear that, as a consequence of the two-dimensional beam fanning, ameasurement value increase is obtained in relation to theone-dimensional beam fanning that took place in the exemplary embodimentof FIG. 2A (which would have only resulted in a single one of the valuegroups “A”, “B”, “C”, . . . ), with the consequence that a comparativelylarge measurement range of focal lengths is covered with, at the sametime, a high resolution. Further, it is clear that, according to FIG.11A, this measurement range increase can also be used for calibrationpurposes by virtue of redundancies namely being created to the extentthat the value groups “A”, “B”, “C”, . . . partly overlap with respectto the respective focal length values in the diagram of FIG. 11A. Infurther embodiments, it is also possible, as illustrated in FIG. 11B andFIG. 11C, to dispense with such redundancies for the benefit of afurther increase of the measurement range of focal lengths coveredoverall, wherein the individual value groups “A”, “B”, “C”, . . . of, ineach case, seven values or points may be produced continuously(according to FIG. 11B) or else with a certain gaps or distances betweenthe value groups “A”, “B”, “C”, . . . (according to FIG. 11C).

The above-described measurement range increase can be used to takeaccount of the large focus variations of the respective beam to becharacterized, as occur, for example in applications of materialprocessing, in particular at high laser powers, as a consequence ofheating and deformation of the individual optical components, namely byvirtue of the “capture region” of the respective focus values beingsignificantly increased (for example, by approximately a factor of sevenaccording to FIGS. 11A-11C) with an unchanged high resolution. Furtherparticularly, this measurement range increase can be used to realize anoverall ISO-compliant beam characterization to the extent thatmeasurement points are obtained in, respectively, a “sufficient” numberor a number that is prescribed by the respective ISO standard, both inthe immediate vicinity of the focus and also at a sufficient distancefrom the focus (e.g. at a distance of two Raleigh lengths) of the beam.

In further embodiments (some of which are schematically illustrated inFIGS. 8A-8E), the diffractive structure involved for the two-dimensionalbeam split may also be obtained in any other suitable manner. Here, thesensor arrangement (e.g. CCD camera) is respectively denoted by “815” inFIGS. 8A-8E.

According to FIGS. 8A-8B, use can also be made of a single diffractiveoptical element 811 or 821, which is already inherently“two-dimensional” (i.e. it has periodic diffractive structures inmutually different, in particular perpendicular directions), instead oftwo diffractive optical elements, and the single diffractive opticalelement may be arranged, in relation to the light propagation direction,either upstream (FIG. 8A) or downstream (FIG. 8B) of the refractiveoptical element 813 or 823 in a beam-splitting optical arrangement 810or 820. According to FIG. 8C, the diffractive structures (which, inturn, extend in mutually different, in particular perpendiculardirections) may also be designed on plano-convex lens elements 831, 832in a beam-splitting optical arrangement 830. According to FIG. 8D, abeam-splitting optical arrangement 840 may also have a diffractiveoptical element 841 with a complex diffractive structure (e.g. as acomplex-encoded CGH), which brings about a diffraction in mutuallydifferent, in particular perpendicular directions, in combination with arefractive lens element 843, wherein, in this configuration too, thediffractive optical element 841 may be alternatively arrangeddownstream, in relation to the light propagation direction, of therefractive lens element 843 as well. According to FIG. 8E, abeam-splitting optical arrangement 850 may also be configured as arefractive lens element 851, which has diffractive structures on bothits light entry face and its light exit face. In all of theabove-described embodiments, the diffractive optical elements ordiffraction gratings may be realized as amplitude gratings, phasegratings or hybrid gratings.

Even though the disclosure has been described on the basis of specificembodiments, numerous variations and alternative embodiments areapparent to a person skilled in the art, for example by combinationand/or exchange of features of individual embodiments. Accordingly, itgoes without saying for a person skilled in the art that such variationsand alternative embodiments are concomitantly encompassed by the presentdisclosure, and the scope of the disclosure is restricted only withinthe meaning of the accompanying patent claims and the equivalentsthereof.

What is claimed is:
 1. A method, comprising: a) splitting a beam in anoptical system into a plurality of partial beams which have a focusoffset in a longitudinal direction in relation to an optical axis; b)recording a measurement image produced by the partial beams; c)performing a forward simulation of the beam in the optical system basedon estimated initial values for beam parameters to obtain a simulatedimage; and d) calculating a set of values for the beam parameters basedon a comparison between the simulated image and the measurement image.2. The method of claim 1, further comprising: e) iteratively performingc) and d), wherein the respectively calculated values for the beamparameters form the basis of a forward simulation that follows in eachcase; and f) outputting output values for the beam parameters,ascertained by the iteration in e).
 3. The method of claim 2, wherein,during the iterative performance of c) and d), the number of varied beamparameters is varied.
 4. The method of claim 2, wherein, during theiterative performance of c) and d), varying an algorithm used in theiteration.
 5. The method of claim 1, further comprising recording anear-field image produced by the beam.
 6. The method of claim 5, furthercomprising, simultaneously with recording the near-field image,recording a far-field image that corresponds to the measurement imageproduced by the partial beams.
 7. The method of claim 1, wherein theplurality of beam parameters comprises at least one member selected fromthe group consisting of beam size, beam decentration, beam inclination,beam divergence, astigmatism, coma and spherical aberration.
 8. Themethod of claim 1, further comprising, based the output values for thebeam parameters, manipulating the beam while adapting at least one ofthe beam parameters.
 9. The method of claim 8, further comprising, inreal time during operation of the optical system, outputting the outputvalues and manipulating the beam while adapting at least one of the beamparameters.
 10. The method of claim 1, wherein a) comprising using abeam-splitting optical arrangement which brings about sphericalwave-front deformations of the beam.
 11. The method as claimed in claim10, wherein the beam-splitting optical arrangement comprises adiffractive structure.
 12. The method of claim 10, wherein thebeam-splitting optical arrangement splits a beam incident on thearrangement into partial beams, and points of incidence of the partialbeams form a two-dimensional, grid-like distribution on a planeextending transversely to the light propagation direction of the beam.13. The method of claim 11, wherein the beam-splitting opticalarrangement comprises two diffractive structures extending in mutuallydifferent directions.
 14. The method of claim 13, wherein thediffractive structures differ by at least a factor of three in terms oftheir focal length related to the first positive order of diffraction ineach case.
 15. The method of claim 1, wherein the beam is a laser beam.16. The method of claim 1, wherein the optical system comprises a laserplasma source.
 17. An apparatus, comprising: a beam-splitting opticalarrangement configured to split a beam incident on the beam-splittingoptical arrangement along an optical axis into a plurality of partialbeams having a focus offset in a longitudinal direction relative theoptical axis; and a sensor arrangement configured to capture the partialbeams wherein the apparatus is configured to be used in the method ofclaim
 1. 18. An arrangement, configured to split a beam incident on thearrangement along an optical axis into a plurality of partial beamshaving a focus offset in a longitudinal direction relative to theoptical axis, wherein points of incidence of the partial beams form atwo-dimensional, grid-like distribution on a plane extendingtransversely to a propagation direction of the beam.
 19. The arrangementof claim 18, comprising two diffractive structures extending in mutuallydifferent directions.
 20. The arrangement of claim 19, wherein thediffractive structures differ by at least a factor of three in terms oftheir focal length related to the first positive order of diffraction ineach case.